FIGS. 5A to 5C show one known physical quantity sensor that detects strains and loads acting on objects (see PTL 1). FIGS. 5A and 5B are a top view and a side view of a conventional physical quantity sensor. In FIGS. 5A and 5B, flexure element 1 is configured with a highly elastic metal material. Hole 2 is punched to form thin stress-concentrating portions 3a to 3d. Notched elongate holes 6a, 6b, 7a, and 7b are provided on stress-concentrating portions 3a and 3b at the top face side of this flexure element 1. These notched elongate holes 6a, 6b, 7a, and 7b are provided along a longer direction connecting fixed end 4 and movable end 5 of flexure element 1, and are connected to hole 2. Notched portions 9 and 10 are formed on the rear face of central beam 8a between notched elongate holes 6a and 7a, and on the rear face of central beam 8b between notched elongate holes 6b and 7b. First piezoelectric element 11 for driving and second piezoelectric element 12 for feedback are bonded at the ends of beam 8b of stress-concentrating portion 3b. 
FIG. 5C is a side view of an essential part where oscillator 13 is connected to portion A in FIG. 5B. As shown in FIG. 5C, first piezoelectric element 11 is connected to an output side of oscillator 13, and second piezoelectric element 12 is connected to an input side of oscillator 13. Resonance frequencies of first and second piezoelectric elements 11 and 12 are selected close to natural frequency fe of beam 8b. 
In the above configuration, when oscillator 13 applies AC voltage with a frequency close to natural frequency fe of beam 8b to first piezoelectric element 11, first piezoelectric element 11 provided at one end of beam 8b generates mechanical vibration. This mechanical vibration causes beam 8b to start vertical string vibration at its natural frequency fe. Second piezoelectric element 12 receives this string vibration, and this second piezoelectric element 12 feeds back an AC signal with a frequency equivalent to natural frequency fe of beam 8b to the input side of oscillator 13. This allows beam 8b to retain string vibration at the frequency equivalent to its natural frequency fe.
If load F acting on movable end 5 of flexure element 1 increases in this state, in which beam 8b is undergoing vertical string vibration, the tensile force on beam 8b increases. This increases natural frequency fe of beam 8b. Conversely, if load F acting on movable end 5 of flexure element 1 decreases, the tensile force on beam 8b decreases. This decreases natural frequency fe of beam 8b. Accordingly, a strain or load F acting on movable end 5 of flexure element 1 can be measured by measuring natural frequency fe output to a terminal.
Advances in microfabrication technology, such as MEMS (Micro Electro Mechanical System) technology, have enabled the creation of extremely small and thin mechanical oscillators. This technology allows configuration of an oscillator itself with small mass, and therefore high-precision oscillators in which frequency or impedance fluctuate widely, in spite of a small load being applied, can be manufactured. By employing this type of micro-mechanical oscillator, a physical quantity sensor that can measure a load or strain acting on the flexure element can be configured just by bonding the physical quantity sensor to the flexure element, without providing a stress-concentrating point on the flexure element itself.
FIGS. 6A to 6C show the conventional physical quantity sensor that inventors of the present invention have created employing an oscillator adopting this MEMS technology. FIG. 6A is a top view of the conventional physical quantity sensor, FIG. 6B is a sectional view taken along line 6B-6B in FIG. 6A, and FIG. 6C is a sectional view taken along line 6C-6C in FIG. 6A. In these FIGS. 6A to 6C, an insulating layer (not illustrated) typically made of an oxide silicon layer or a silicon nitride layer is formed on the surface of semiconductor substrate 101. Beam 102 is formed by etching semiconductor substrate 101. Fixed portion 103 surrounds beam 102. Driving element 104 is formed on a central portion of the surface of beam 102. Driving element 104 includes a lower electrode (not illustrated), a piezoelectric layer (not illustrated) typically made of PZT, and an upper electrode (not illustrated) in this sequence from the bottom. Furthermore, feedback element 105 is formed at an end of beam 102. Feedback element 105 includes a lower electrode (not illustrated), a piezoelectric layer (not illustrated) formed of PZT, and an upper electrode (not illustrated) in this sequence from the bottom. Driving element 104 and feedback element 105 are electrically connected to land 106 by a wiring pattern (not illustrated). The oscillator is connected and fixed by rigid substance 108, such as a metal bonding material for Au—Au bonding and epoxy resin, onto fixed portions 103 at both ends of beam 102 so that a strain generated in flexure element 107 is transmitted to the oscillator.
Driving element 104 is connected to the output side of an amplifier (not illustrated), and feedback element 105 is connected to the input side of the amplifier via a phase shifter (not illustrated). Resonance frequencies of driving element 104 and feedback element 105 are selected close to natural frequency fe of beam 102.
In the above configuration, when the amplifier applies AC voltage with a frequency close to natural frequency fe of beam 102 to driving element 104, driving element 104 generates mechanical vibration. This mechanical vibration makes beam 102 start vertical string vibration at natural frequency fe. Feedback element 105 receives this string vibration, and feeds back an AC signal with frequency equivalent to natural frequency fe of beam 102 to the input side of the amplifier via the phase shifter. Accordingly, beam 102 retains the string vibration at a frequency equivalent to its natural frequency fe.
If load f acting on flexure element 107 increases in this state in which beam 102 is undergoing vertical string vibration, the tensile force on beam 102 increases. Natural frequency fe of beam 102 therefore increases. Conversely, if load f acting on flexure element 107 decreases, the tensile force on beam 102 decreases, and natural frequency fe of beam 102 therefore decreases. In this way, a strain or load f acting on flexure element 107 can be measured by measuring natural frequency fe output to the terminal.
However, in the conventional physical quantity sensor in FIGS. 5A to 5C, beam 8b tends to generate a higher-order resonance mode, such as 3rd harmonic and 5th harmonic resonance modes, since first piezoelectric element 11 for driving is attached to the end of beam 8b. This higher-order resonance mode has a low Q factor, which shows sharpness of resonance, compared to the fundamental vibration mode that is the lowest mode of vibration in which the center of beam 8b is an antinode and both ends are nodes. Coupling of higher-order modes is also likely to occur. The vibration frequency of beam 8b may thus change significantly if the ambient temperature or power voltage applied to oscillator 13 changes. In some cases, this causes a failure to accurately measure a strain or load F acting on movable end 5 of flexure element 1.
On the other hand, in the conventional physical quantity sensor shown in FIGS. 6A to 6C, driving element 104 is formed at the center of beam 102. The fundamental vibration mode is therefore generated in beam 102. However, feedback element 105 is formed only on one end of beam 102. This makes the vibration mode asymmetric relative to the center of beam 102, due to the difference in rigidity between feedback element 105 and beam 102 or the mass of feedback element 105. FIG. 7 illustrates the results of simulating the distribution of vibration displacement when driving element 104 that is 3 μm thick and 0.45 mm long, and feedback element 105 that is 3 μm thick and 0.2 mm long, are formed on beam 102 that is 10 μm thick and 1.2 mm long. As shown in FIG. 7, the fundamental vibration mode is generated in beam 102, in which the center is the antinode and both ends are nodes. However, the maximum amplitude is shifted to the left from the center of beam 102. This asymmetry mode has a low Q factor, which shows sharpness of resonance, compared to the symmetric mode. This reduces amplitude in feedback element 105, thus reducing the accuracy of vibration frequency. The output charge generated in feedback element 105 is also reduced. Accordingly, the measurement accuracy of a strain or load f acting on flexure element 107 may degrade.